I don't really get this example - whatever the tone of voice, I think I would understand "quite well" as "fairly well, reasonably well, less well than well" to some degree. Similarly with "quite a lot". OTOH I think there are adjectives and adverbs which can be modified by "quite" in two opposed ways - it either means "completely" or "partially". For instance, "quite charming(ly)" could be ambiguous out of context, meaning either "completely charming" (highest pitch on "quite", then a gradual fall over "charming" for me) or "fairly charming" (lower pitch on "quite" here, followed by dip and rise over "charming"). Maybe this was what you meant too? But it doesn't work for all words that "quite" might modify, for me anyway.

Hmm, yes, the more positive sound definitely has '(low pitch) quite (higher pitch) well' - there is a feeling of being pleased, and perhaps surprised, to it. Whereas the more negative sound has (I think) about the same pitch but the 'quite' is extended in time; it feels conditional, 'could have done better', maybe a little disappointed though not seriously upset or dissatisfied.

I agree that the first one would imply doing better than expected (and certainly better than the second one) - but I wouldn't see it as being better than just "well". (It also doesn't have the "completely" meaning I was talking about earlier, which is probably a separate issue.) Similarly, while "quite a lot" could cover a range of quantities, some unexpectedly large, I don't think I'd use it (or understand it generally) to mean more than "a lot". There would be a sort of scale (for me) including items like:"quite a lot" (not very much)"quite a lot!" (rising pitch, surprise implied)"a lot""a lot!" (similar rising pitch)"really a lot"

There's also a transatlantic difference here - in the US, "quite" is often used as an intensifier rather than a limitation. This has been known to cause miscommunications between one of my partners and the rest of our social group.

I suppose it may depend a little on the speaker, because some people do use 'quite' as more of an intensifier. It may also depend on the phrase... I mean, if you said 'That's quite brilliant!', wouldn't that sound more brilliant than 'That's brilliant!'? Or maybe it wouldn't. Maybe that does just depend on who's speaking... *shrug*

Interestingly, the comparative in Latin can be translated as 'quite' (or 'rather'), which makes you wonder exactly what use of 'quite' you're employing when you're translating. In Latin the general consensus is that it is an intensifier though.

"Quite a lot" can be more than "a lot". With "quite a lot" the speaker is perhaps implying that they have a larger frame of reference and that they've seen this sort of thing several times before so it sounds more impressive than "a lot" which in turn sounds vague, immature and badly informed. Perhaps by deliberately reducing the "a lot" with "quite" it means more.